The use of forward error correction codes, for example, turbo codes or Low Density Parity Check (LDPC) codes, is well known in data communication and, in particular, for wireless communication, to give improved performance in terms of bit error rate as a function of received Signal to Noise Ratio (SNR). Such codes may be binary codes, based on a series of binary code symbols, that is, symbols that may each have one of two values. Such symbols may be termed GF symbols, where the magnitude of the GF is 2, so that each symbol includes a single bit. Each bit is mapped to a physical layer code-word of the wireless system, such as a constellation symbol and/or a Multiple-Input Multiple-Output (MIMO) code-word, for transmission, and on reception, it is required to de-map received signals onto GF symbols. This mapping is straightforward in the case of binary codes.
Non-binary forward error correction codes have also been proposed, such as non-binary turbo codes and non-binary low density parity check codes. These are based on a series of GF symbols that may be transmitted with a value selected from more than two values, that is, the symbols are GF symbols with a GF of magnitude greater than 2. This may give higher performance in terms of error protection than conventional binary codes. A GF symbol may, for example, have 64 potential states, so that the symbol may be represented by 6 bits (i.e., 26). However, the mapping and de-mapping of GF symbols to and from physical layer code-words may be complex and problematic.
For soft decision decoding of a binary code, each received GF symbol of a transmitted forward error correction code-word is typically given an associated likelihood estimate, that is, a likelihood that the symbol was transmitted with a particular binary state, based on properties of the received signal. A likelihood is associated with a degree of confidence in the state of a symbol. Not all symbols will be received with the same confidence, due, to, for example, propagation conditions of radio signals and/or noise and interference conditions at a receiver. Improved error correction performance may be realized by taking into account the likelihood of each state of each symbol in the decoding of the forward error correction code.
Soft decision decoding of non-binary codes typically requires a number of likelihood estimates per symbol that is equal to the number of possible states of the symbol. A likelihood estimate, and, in particular, a Log Likelihood Estimate (LLE), may, for example, be derived from the comparison of a received signal vector with locations on a grid of constellation points used for the detection of a constellation symbol, that is, a Euclidean distance.
Mapping and de-mapping of non-binary codes to the physical layer (specifically, to physical layer code-words) may result in complexity, particularly in terms of de-mapping at the receiver that may be prohibitive.
In the case of a one-to-one correspondence between the number of bits representing a GF symbol and a physical layer code-word, typically one distance is required to be calculated in determining each likelihood estimate for decoding a GF symbol. For other relationships, multiple Euclidean distances may need to be calculated for each Log Likelihood Estimate (LLE) and the de-mapping process may be computationally demanding. However it may be limiting in terms of physical implementation to restrict the relationship to a one-to-one correspondence.